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<p>We consider the Novikov problem of describing the level lines of quasiperiodic functions on a plane for two-dimensional potentials of dihedral symmetry. We show that the quasiperiodic potentials under consideration can have open level lines only at a single energy level <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\( \epsilon = \epsilon _{0} \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>ϵ</mi> <mo>=</mo> <msub> <mi>ϵ</mi> <mn>0</mn> </msub> </mrow> </math></EquationSource> </InlineEquation>, which also brings them closer to random potentials on a plane. Bibliography&#xa0;:&#xa0; 10 titles. Illustrations&#xa0;:&#xa0; 9 figures.</p>

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THE NOVIKOV PROBLEM FOR DIHEDRAL SYMMETRY POTENTIALS

  • 期刊论文

  • 发表日期：

    2025年11月1日

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  • A. Ya. Maltsev

摘要

We consider the Novikov problem of describing the level lines of quasiperiodic functions on a plane for two-dimensional potentials of dihedral symmetry. We show that the quasiperiodic potentials under consideration can have open level lines only at a single energy level \( \epsilon = \epsilon _{0} \) ϵ = ϵ 0 , which also brings them closer to random potentials on a plane. Bibliography :  10 titles. Illustrations :  9 figures.